Multi-phase composite synchronization of three vibrators in a space far-resonant vibration system.

To improve the problem that self-synchronization and control synchronization of vibration systems are respectively restricted by their inherent characteristics and product cost, by combining them a multi-phase composite synchronization scheme is proposed for space far-resonant vibration system actuated by three vibrators. Based on the established mathematical model and sliding mode control (SMC) algorithm, controller of one vibrator is designed to implement the multi-phase control synchronization. Then self-synchronization mechanism of the other two vibrators is analyzed through small parameter average method and Routh-Hurwitz criterion. Besides, necessary calculation and simulation cases in multi-phase composite synchronization state are further conducted. Research results indicate that the multi-phase composite synchronization of three vibrators can be carried out in stable operation regions, but chaotic behaviors, since severe mass asymmetry of the eccentric rotors (ERs), will be induced when the phase differences (PDs) between two coaxial vibrators are controlled in -1.99∼-1.67 and 1.63∼2.1 (rad), and the controlled PDs around -0.4 (rad) should be avoid to ensure a stronger synchronization ability.

Unleashing the mechanism between small and medium enterprises, and green financing in China: a pathway toward environmental sustainability and green economic recovery.

In this research, we analyzed green finance, small and medium-sized businesses, and financial literacy in China to boost the green economy. Green finance and financial literacy were examined holistically using a rigorous empirical approach and data envelopment analysis to provide the way to advance green economic recovery in this research. According to empirical evidence, green financing impacts SMEs at 0.31, 0.41, and 2.02 on green economic recovery. China's green finance and small businesses contribute significantly to the country's overall green economic revival. A more accurate forecast of green economic recovery was made possible by including other variables such as population expansion, development, and small business development. The analysis used the data envelopment analysis, and the results were solid. Additional hypothetical time-dependent instances demonstrated China's predicted green financing and small business's nexus for 2000 to 2020. The proportion of SMEs is decreasing, and as a result, green financing and financial literacy have increased by an average of 12.5% during this time. China's green financing would fall dramatically if the country's industrial structure is reduced. According to our findings, financial literacy is positively correlated with green economic recovery, while illiteracy is negatively correlated with growth. Finally, the report provides some ideas for China's future green economic recovery.

Synchronization of two homodromy rotors installed on a double vibro-body in a coupling vibration system.

A new mechanism is proposed to implement synchronization of the two unbalanced rotors in a vibration system, which consists of a double vibro-body, two induction motors and spring foundations. The coupling relationship between the vibro-bodies is ascertained with the Laplace transformation method for the dynamics equation of the system obtained with the Lagrange's equation. An analytical approach, the average method of modified small parameters, is employed to study the synchronization characteristics between the two unbalanced rotors, which is converted into that of existence and the stability of zero solutions for the non-dimensional differential equations of the angular velocity disturbance parameters. By assuming the disturbance parameters that infinitely approach to zero, the synchronization condition for the two rotors is obtained. It indicated that the absolute value of the residual torque between the two motors should be equal to or less than the maximum of their coupling torques. Meanwhile, the stability criterion of synchronization is derived with the Routh-Hurwitz method, and the region of the stable phase difference is confirmed. At last, computer simulations are preformed to verify the correctness of the approximate solution of the theoretical computation for the stable phase difference between the two unbalanced rotors, and the results of theoretical computation is in accordance with that of computer simulations. To sum up, only the parameters of the vibration system satisfy the synchronization condition and the stability criterion of the synchronization, the two unbalanced rotors can implement the synchronization operation.